Vortex shedding flowmeter

ABSTRACT

A flowmeter for measuring the velocity of fluid flow by monitoring the vortex shedding frequency of the fluid flow comprises a single mode optical fibre sensing element (1) for detecting vortex shedding and utilizes interferometric techniques for producing an electrical output signal corresponding to the vortex shedding frequency. The sensing element (1) comprises at least part of the signal arm (2) of an interferometer (3) which also includes means (12) for deriving a reference signal from the illuminating light source (4). The flow induced oscillation of the sensing element (1) caused by vortex shedding produces modulations of the interferometer output which is monitored by a photodetector (14) which, in turn, produces a modulated electrical output signal which can be processed by a signal processing system (16-19) to identify the vortex shedding frequency and, hence, produce a measurement of the flow velocity.

BACKGROUND OF THE INVENTION

The present invention relates to a flowmeter for measuring the velocityof flow of a fluid, such as, a liquid, gas or vapour phase, by detectingthe vortex shedding frequency of the fluid flow and, more particularly,to such a flowmeter which utilises a fibre optic sensing element todetect vortex shedding.

Flow rate measurement based on the natural phenomenon of vortex sheddingis known and has been realised using a variety of techniques formonitoring the vortex shedding frequency. When a bluff (that is,non-streamlined) body is sited in a fluid flow, it will, under certainconditions, cause a regular stream of vortices to form in the fluiddownstream of the body. These vortices leave alternately from oppositesides of the body. Moreover, as each vortex is generated and shed, itproduces a lateral force on the body and, if the body is sufficientlyflexible, it will oscillate.

The pattern of flow past the bluff body is governed by the Reynoldsnumber (Re). The transition from a steady laminar flow to an unsteadyturbulent flow occurs at Re˜40. For Re>40 wakes appear behind the bodyand eddies are formed. When Re exceeds 100, the boundary layer separatesand the eddies are shed alternately from opposite sides of the body,resulting in the Karman vortex sheet. This vortex shedding occurs with aregular periodicity in the turbulent flow region, except in thetransition regions when 200<Re<400 and 3×10⁵ <Re<3×10⁶. This breakdownis mainly due to transition from a laminar to a turbulent boundary layerstate.

The vortex shedding frequency f is related to the flow velocity v by theequation

    f=sv/d

where s is the Strouhal number and d is the diameter of a cylindricalbluff body. Generally s is a function of the Reynolds number, and thestudy of the flow velocity dependence of s is an established branch ofresearch in hydrodynamic studies. For large values of Re the turbulenceof the vortices has a stabilising effect on the value of s and it iseffectively constant. Hence, the flow velocity may be directlydetermined from a measurement of the vortex shedding frequency.

The linearity and wide dynamic range of the vortex shedding process havebeen exploited in a number of commercial flowmeter designs. Vortexshedding detection techniques include temperature, pressure and strainsensing, with the sensing element either being sited on the bluff bodyor being disposed down the vortex sheet. Also, a flowmeter of this typehas been proposed which uses a multimode optical fibre sensing element,as the bluff body, and in which the oscillating strain induced in thefibre sensing element, as a result of the vortex shedding effect, isdetected by the fibredyne technique. This proposal is described in thepublication "Electronics Letters" of Mar. 19, 1981 at page 244. Thefibredyne technique suffers from random fading and the generation oflarge numbers of harmonics of the fundamental pertubation. Whilst thetechnique adequately determines the vortex shedding frequency, it showsthe harmonics of the fundamental frequency in the output spectrum anddoes not give the absolute amplitude of the strain.

SUMMARY OF THE INVENTION

It is an object of the present invention to avoid the problemsexperienced with the previously proposed arrangement of fibre opticvortex shedding flowmeter and to provide such a flowmeter having asingle mode optical fibre sensing element and utilising interferometricmonitoring techniques.

To this end, the invention consists in a flowmeter for monitoring thevortex shedding frequency of a fluid flow, comprising a tensionedoptical fibre sensing element arranged to extend transversely to thefluid flow so as to oscillate in response to vortex shedding, a lightsource for illuminating the optical fibre, and a photodetector forsensing the interference pattern at an output of the fibre sensingelement and producing an electrical signal corresponding to the vortexshedding frequency, characterised in that the sensing element comprisesat least part of a single mode optical fibre forming the signal arm ofan interferometer which also includes means for deriving a referencesignal from the illuminating light source, said interferometer producingan interference signal which corresponds to the optical phase differencebetween the signal light beam and the reference signal and which ismodulated by oscillation of the sensing element in response to vortexshedding, and said photodetector being arranged to sense theinterference signal and produce an electrical signal having a modulationfrequency corresponding to the vortex shedding frequency.

With the invention, the sensing element part of the monomode opticalfibre signal arm may be stretched across a flow tube or passage suchthat the process of vortex shedding induces an oscillating strain in thesensing element which vibrates in alternate directions normal to itsaxis. The strain is detected by monitoring the interferometer irradianceusing the photodetector, the output of which may be processed to producean electrical signal identifying the vortex shedding frequency and,hence, the flow velocity. Signal processing means for optical fibreinterferometers are known which are capable of recovering from theelectrical output signals of the photodetector, the absolutestrain-induced phase changes with extreme sensitivity and over a widedynamic range.

In one embodiment, the interferometer of the flowmeter has a Fabry-Perotconfiguration. It is formed between the normally cleaved input anddistal faces of the single mode optical fibre, the length of which isselected so that the visibility of the interference fringes ismaximised. The interferometer is used in reflection and the outputirradiance is monitored by the photodetector. The vortex sheddingfrequency is determined from the modulation frequency of thephotodetector output and is derived from a counting system whichregisters the number of positive or negative-going transitions throughan adjustable discriminator level. The number of counts registered perfibre oscillation is a function of the flow velocity, fibre tension andequilibrium operating point of the interferometer. By using dataacquisition times of a few seconds, thermal effects causing randomdrifts of the interferometer operating point may be averaged. Thevelocity dependence may be determined by calibration experiments. Thecalibration is highly reproducible and stable and permits thedetermination of the flow velocity over a wide range of fibre Reynoldsnumber.

The time-averaging technique is used to alleviate inaccuracies whichmight otherwise be caused by the environmentally induced drift in theinterferometer operating point. This technique in turn limits theresponse time of the flowmeter. Alternatively, an active homodyne signalprocessing system may be employed which maintains the interferometer ata constant operating point, conveniently, in quadrature. Such aprocessing system is capable of detecting much smaller phase changes, soextending the dynamic range of the flowmeter. It is equally applicableto flowmeters according to the invention embodying a Fabry-Perot,Michelson, Mach-Zehnder or Polarimetric interferometer

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the present invention may be more readily understood,reference will now be made to the accompanying drawings, in which:

FIG. 1 diagrammatically illustrates one embodiment of the inventionbased on a Fabry-Perot interferometer,

FIG. 2 is a graph illustrating results achieved with the embodiment ofFIG. 1,

FIG. 3 diagrammatically illustrates a second embodiment based on anall-fibre Michelson interferometer,

FIG. 4 is a graph illustrating the results achieved with the embodimentof FIG. 3, and

FIGS. 5A-D illustrate typical recorded vortex shedding signals for thehomodyne detection system of FIG. 3 and show the effect of reducing thetension in the optical fibre sensing element.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIG. 1 of the drawings, the flowmeter comprises a sensingelement 1 which is part of a single mode optical fibre 2 forming thesignal arm of a Fabry-Perot interferometer 3. The latter is formedbetween the normally cleaved input and distal ends 12,15 of the fibreand is illuminated by a coherent light source 4, for example, a 0.5 mWmulti-mode helium-neon laser. The fibre sensing element 1 is disposeddiametrically across a flow tube 5 for fluid, the flow rate of which isto be measured. It is mounted between two clamps 6,7 and is tensioned bya tensioning element 8 supporting the clamp 7. It is sealed in theopenings via which it extends through the flow tube 5 by flexible fillermaterial 9.

Light from the coherent source 4 is launched into the optical fibre 2via a beam splitter 10 and a collimating lens 11 which focusses thelight beam onto the input end 12 of the fibre. The latter is reflectiveand a fraction of the incident light is reflected from the end face 12as a reference beam. The latter is collimated by the lens 11 and isreflected by the beam splitter 10, via a second collimating lens 13,onto a photodiode detector 14. The fraction of the input beam propagatedwithin the fibre 2 is guided to the distal end 15, which is silvered soas to reflect the beam back through the fibre. The returning signalbeam, similarly to the reference beam, is collimated by the lens 11 andis reflected by the beam splitter 10, via the lens 13, onto thephotodiode 14. It mixes coherently with the reference light beamsreflected from the input end face 12 of the optical fibre 2 to producean interference signal. The photodiode detects this interference signaland produces an electrical current output I which is of the form I₀(1+cos φ), where φ corresponds to the optical phase delay between thereference and signal light beams introduced by passage of the latterthrough the fibre 2. As is hereinafter more fully described, thisphotodiode output is supplied to a signal processing system comprisingan amplifier 16, a band-pass filter 17, a discriminator 18 and a counter19.

Upon the flow of a fluid, for example, water, through the tube 5, vortexshedding occurs alternately from opposite sides of the sensingelement 1. This induces an approximately simple harmonic oscillatingstrain of amplitude a(v) in the sensing element, which vibrates inopposite directions normal to its axis. The strain amplitude is afunction of the flow velocity v. It produces an optical phase ofmodulation amplitude Δφ(v) in the beam guided in the fibre 2 and, hence,modulates the photodetector output I. The vortex shedding frequency f isdetermined from the frequency spectrum of I, which comprises harmonicsof a fundamental frequency 2f. The distribution of power amongst theharmonics is determined by Δφ(v) which may hence be derived.

In the embodiment shown in FIG. 1, the vortex shedding frequency f isdetermined by using a simple counting system which provides a practicaland inexpensive signal processing system. The output from the photodiode14 is amplified at 16 and then fed to the band-pass filter 17. Thediscriminator 18 and counter 19 are used to determine the number ofpositive-going transitions through the discriminator level per unit timef. The number of counts recorded per sensing element oscillation is 2n,where n may take either of the integral values in the range

    [Δφ(v)/2π-1]<n(v)≦[Δφ(v)/2π+1]

depending on the equilibrium operating point of the interferometer 3 andthe discriminator level set. The operating point of the interferometerdrifts randomly due to environmentally induced phase changes, arisingchiefly from thermal effects. By using sufficient counting time, forexample of a few seconds, frequencies which depend on the time-averagedvalue <n(v)>, are obtained and which are substantially independent ofthe instantaneous operating point of the interferometer. The functionaldependence <n(v)> is determined by calibration. The vortex sheddingfrequency and, hence, the flow velocity are thus determined.

Utilising the above flowmeter, tests have been carried out on three flowtubes 5 of 0.4 m in length and with internal diameters of 20, 10 and 6.5mm, respectively, to achieve a large range of Reynolds number. A singlemode optical fibre sensing element 1 was positioned along a diameter atthe centre of each tube 5 to avoid end effects. Vortex shedding inducedan oscillating strain whose amplitude a(v) is a function of the flowvelocity v. This oscillating strain produced an optical phase ofmodulation amplitude Δφ(v) in the beam guided in the fibre 2. The phasemodulation was determined interferometrically using the constructiondescribed above. The water flow through the tube was driven by animpeller pump (volume rate up to 1 l/s) which was vibration isolatedfrom the flow tube using flexible tubing to minimise vibration and thepropagation of pressure waves from the pump. Further damping wasprovided by a large reservoir between the pump and the inlet tube.Interferometric measurements were employed to check the contribution ofpossible mechanical and hydraulic vibrations and these were found to benegligible. No signal was observed at the frequency of the pump (equalto the pump rotational frequency multiplied by the number of impellers).

The functional dependence <n(v)> was derived from experimental dataprovided by the above tests for the variation of f with v and wasconfirmed by measuring f as a function of v directly using a spectrumanalyser. Theoretical considerations had predicted strain amplitudes upto 10λ and these were observed. The calibration was highly reproducibleand stable and permitted the determination of f over a wide range ofReynolds number, as shown in FIG. 2, which compiles data obtained fromall three flow tubes; these data are consistent with the relationshipf=sv/d using s=0.2. The time-averaging technique also allowed operationin the lower transition range, into which the data shown in FIG. 2extend.

The embodiment illustrated in FIG. 3 is based on an all-fibre Michelsoninterferometer 20. The latter comprises a single mode optical fibresignal arm 21, a part of which forms the sensing element 22, and asingle mode optical fibre reference arm 23. The distal end faces 24,25of both fibre arms are silvered. The sensing element 22 is mounted,under tension, diametrically across the flow tube 26, in a similarmanner to the optical fibre of FIG. 1 by clamps 27,28, a tensioningelement 29 and flexible filler material 30. The fibre reference arm 23is coiled about an electrical piezoelectric crystal 31 excited by aservo system which is hereinafter more fully described and is arrangedto compensate for differential phase drifts between the interferometerarms 21, 23 caused by environmental perturbations, such as, temperaturefluctuations.

Light from a coherent light source 32, for example, a multimodehelium-neon laser, is launched into a single mode input fibre 33 of theinterferometer, via a lens 34, and is amplitude divided by a single modebidirectional fusion coupler 35 into the interferometer signal andreference arms 21,23. The light beams guided in the two arms arereflected from the distal ends 24,25 thereof and the returning beams aremixed by the fusion coupler 35 and guided by a single mode output fibreto a photodiode detector 37 which senses the resulting intereferencesignal and produces an electrical output signal which is fed, via anamplifier 38, to a homodyne signal processing system comprising aspectrum analyser 39. Mode strippers 40 may be associated with the inputand output fibres 33, 36.

The embodiment described with reference to FIG. 1 uses time-averagingtechniques in order to compensate for environmentally induced drift ofthe interferometer operating point. This limits the response time of theflowmeter. To alleviate this drawback, the embodiment of FIG. 3 employsan active homodyne signal processing system which maintains theinterferometer at a constant operating point, normally, in quadrature.This system is capable of detecting much smaller phase changes, soextending the dynamic range of the flowmeter. Moreover, whilst describedin conjunction with a Michelson configuration, the system employed inthe embodiment of FIG. 3 is equally applicable to flowmeters embodyingFabry-Perot, Mach-Zehnder and Polarimetric configurations.

The compensating circuit illustrated in FIG. 3 is fully described in apaper by D. A. Jackson entitled "Elimination of drift in a single modeoptical fibre interferometer using a piezoelectrically stretched coiledfibre" published in Applied Optics, Volume 19, 1980 at page 2926, and itwill not therefore be described hereafter in detail. Briefly, itcomprises a comparator 41, a low pass filter 42 and an integrator 43,including a high voltage amplifier, and produces an error signal whichis proportional to the drift of the interferometer operating point andwhich is used to excite the piezoelectric crystal 31 so as to strain thereference arm 23 in such a manner as to compensate for the drift. Withthe interferometer operating at quadrature, the vortex shedding signalis monitored by analysing the frequency spectrum of the photodiode 37output. The interferometer irradiance is given by

    I=A{1+cos [φ.sub.d +φ.sub.m sin (ωt)]}

where φd is the quasi-static phase difference, φ_(m) is the amplitude ofthe phase change induced by the vortex shedding, ω=2πf and A is aconstant.

When operating at quadrature, the interferometer irradiance can bewritten in terms of the Bessel functions J_(n) (φ_(m)) as ##EQU1##Clearly only the odd harmonics contribute. The maximum vortex-sheddinginduced phase change is measured to be about 1 rad which means thecontribution from the fundamental component dominates with the ratio J₃/J₁ ≦5 percent in most cases.

FIGS. 5A to 5D show the frequency spectra of typical recorded vortexshedding signals utilizing the active homodyne detection systemdescribed above, with small strain amplitudes. The three sets of spectraof FIGS. 5A, B and C relate to the same flow velocity but were obtainedwith different applied tensions in the fibre sensing element 22. Theeffect of reducing the tension in the fibre and, hence, increasing thestrain amplitude induced by vortex shedding, is an increase in therecorded vortex-shedding signal amplitude accompanied by spectralbroadening. Reducing the tension further, causes the excitation of thefibre resonant frequency for transverse oscillations, as can be seen inFIG. 5D. Because of the increased oscillating strain amplitude theexpected third harmonic of the vortex shedding frequency can also beseen.

When the vortices are shed parallel and normal to the axis of the fibresensing element, the shedding occurs in-phase resulting in a sharplypeaked signal, as in the high tension case (FIG. 5A). However, when theyare shed from a curved body, such as a slack fibre which has bowed dueto the water flow, anharmonic shedding and the resulting phasedifference effects give rise to signals showing an increased noiselevel.

Data compiled for the flowmeter of FIG. 3 by conducting tests on threeflow tubes of the same dimensions and under the same conditions as theflow tubes used to obtain the test results for the flowmeter of FIG. 1are shown in the graph of FIG. 4. The recorded vortex shedding frequencyvariation with flow velocity was linear and the conformity of the datain the normal operating range was better than 2%. The graphicallycalculated value of the Strouhal number (given by the slope of thegraph) agrees with its expected value for the Reynolds number rangeconsidered. The Strouhal number varies continuously from about 0.12-0.19when the Reynolds number increases from about 60-600 for a smoothcylinder. However, the roughness of the body has a stabilising effect onthe Strouhal number. The FIG. 3 embodiment was successively operated inthe lower transition region. Irregularity in this region arises frominstability of the vortex street to the three-dimensional disturbances.However, since the vortices are detected on the sensing element at theinstance of the shedding, the recorded signals are clear.

Whilst particular embodiments have been described, it will be understoodthat modifications can be made without departing from the scope of theinvention as defined by the appended claims. For example, the fibresensing element 1 or 22 may be exposed directly to the flow or may bebonded to or mounted within a suitable bluff body which has someflexibility and which serves as a protective shield for the fibre.Moreover, the beam splitter 10 shown in FIG. 1 may be replaced by anoptical fibre directional coupler to produce a functionally identicalsystem.

We claim:
 1. In a flowmeter for monitoring the vortex shedding frequencyof a fluid flow, said flowmeter comprising a tensioned optical fibresensing element arranged to extend transversely to the fluid flow so asto oscillate in response to vortex shedding, a light source forilluminating the optical fibre, and a photodetector for sensing anoutput of the fibre sensing element and producing an electrical signalcorresponding to the vortex shedding frequency, the improvement whereinsaid sensing element comprises at least part of a single mode opticalfibre forming a signal arm of an interferometer which also includesmeans for deriving a reference signal from the illuminating lightsource, said interferometer producing an interference signal whichcorresponds to the optical phase difference between the signal lightbeam and the reference signal and which is modulated by oscillation ofthe sensing element in response to vortex shedding, and saidphotodetector being arranged to sense the modulated interference signaland produce an electrical signal having a modulation frequencycorresponding to the vortex shedding frequency.
 2. A flowmeter accordingto claim 1, wherein the optical fibre signal arm has said part thereofforming the sensing element under tension and extending transverselythrough a flow channel for guiding the fluid flow about the sensingelement.
 3. A flowmeter according to claim 1, wherein the interferometerhas a Fabry-Perot configuration in which the optical fibre signal armhas reflective input and distal ends, whereby the light sourcepropagates a signal light beam within the signal arm which is reflectedfrom the distal end thereof for mixing with a reference signal reflectedfrom the input end of the signal arm and producing the interferencesignal.
 4. A flowmeter according to claim 1, wherein the interferometerhas a Michelson configuration and comprises separate single mode opticalfibre signal and reference arms having reflective distal ends, and meansat the input ends of the fibre arms for launching the light from thelight source into the arms and for mixing the reflected light beamspropagated in the arms to produce the interference signal.
 5. Aflowmeter according to claim 4, wherein the mixing means comprises abi-directional coupler, the light from the light source is arranged tobe launched into the two arms of the interferometer by an input opticalfibre coupled to the input of the bi-directional coupler, and theinterference signal at the output of the coupler is guided to thephotodetector by an output optical fibre.
 6. A flowmeter according toclaim 1, further comprising signal processing means for monitoring theoutput of the photodetector and producing an output signal identifyingthe vortex shedding frequency, said processing means including countingmeans which counts the number of transitions in the photodetector outputsignal through an adjustable discriminator level.
 7. A flowmeteraccording to claim 1, further comprising signal processing means formonitoring the output of the photodetector and producing a signalidentifying the vortex shedding frequency, said processing means being ahomodyne signal processing means for maintaining the interferometer at aconstant operating point.
 8. A flowmeter according to claim 7, whereinthe processing means includes compensating circuit means for producingan error signal proportional to the drift of the interferometeroperating point, and means responsive to the error signal for adjustingthe reference signal to compensate for the drift of said operatingpoint.
 9. A flowmeter according to claim 8, wherein the reference signalis propagated in an optical fibre reference arm of the interferometerand the means responsive to the error signal for adjusting the referencesignal is arranged to adjust the strain applied to the reference arm.